1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mumz [18]
3 years ago
11

How do I solve this three variable equation

Mathematics
2 answers:
KengaRu [80]3 years ago
7 0
A) 2.x - 6.y + z = 30
b) -x  + 3.y +2.z = - 20
c) -6.x -5.y +6.z = 7

1st, let's take a) and b) alone and let's eliminate x

a) 2.x - 6.y + z = 30
b) -x  + 3.y +2.z = - 20

2nd) multiply b) with 2 and once done add a) with the result of b):
b') times 2 → -2.x+6.y+4.z = - 40. Now add it to a):

a) 2.x - 6.y + z = 30
b') -2.x+6.y+4.z = - 40
+  -----------------    -----
     0.x + 0.y + 5.z = -10    → z = -2

Now replace z with its value (-2) in :

b) -x  + 3.y +2.z = - 20  → - x + 3.y -4 = -20 → - x +3.y = -16
c) -6.x -5.y +6.z = 7 → -6.x - 5.y -12 = 7 → - 6.x -5.y = 19

Consider the result of:
- x +3.y = -16  and
- 6.x -5.y = 19
Now let's eliminate x from both equations.
To that end multiply the 1st one by (-6)
6x - 18y = 96  and add it to - 6.x -5.y = 19

6x - 18y = 96
-6.x -5.y = 19
+---------    ----
0.x - 23.y   115  → 23y = -115 and y = -115/23 = - 5→→ y = -5

Now that you have the value of z= - 2 and y = -5, plugin in any of the equation and you will find x = 1. So the final result is:
 x = 1 ; y = - 5  ; and z = - 2

vodomira [7]3 years ago
4 0
2x - 6y + z = 30      (1st)
-x + 3y + 2z = -20 (2nd)
-6x - 5y + 6z = 7   (3rd)

from (2nd)  you have:
-x + 3y + 2z = -20 
 x = 3y + 2z + 20

substitute x = 3y + 2z + 20 into  (1st) 2x - 6y +z = 30

2x - 6y + z = 30
2(3y + 2z + 20) - 6y +z = 30
6y + 4z + 40 - 6y + z = 30
5z + 40 = 30
5z = -10
  z = -2

plug in z = - 2 into (2nd) and  (3rd)

-x + 3y + 2(-2) = -20 (2nd)
-x + 3y = -16 so x = 3y + 16

-6x - 5y + 6z = 7   (3rd)
-6x -5y +6(-2) = 7
-6x - 5y = 19

substitute x = 3y + 16 into -6x - 5y = 19

-6x - 5y = 19
-6(3y + 16) - 5y = 19
-18y - 96 - 5y = 19
-23y = 115
     y = -5

x = 3y + 16
x = 3(-5) + 16
x = -15 + 16
x = 1

answer
x = 1, y = -5 and z = -2



You might be interested in
The ratio of people who walk home from school to people who ride the bus home is 2 : 7. The number of bus riders is how many tim
Strike441 [17]
The number of bus riders is 3.5 times the number of walkers.
6 0
3 years ago
Read 2 more answers
Polygon ABCDEF is a regular polygon. If point O is located at the center of the polygon, what degree of rotation about point O w
4vir4ik [10]
60° , 360° , 720° , and 300° hope i helped and have a great reast of the week and weekend
5 0
3 years ago
I NEED HELP PLEASE I
Juli2301 [7.4K]

Answer:

10x+40

Step-by-step explanation:

To solve you must follow these steps:

1. Multiply the outside (5) by the first number on the inside (2x) and you get 10x

2. Multiply the outside (5) by the second number on the inside of the parenthesis (8) and you get 40

3. You are left with 10x and 40, so your answer is 10x+40

Hope this makes sense, have a wonderful day!

4 0
3 years ago
Read 2 more answers
A model rocket is launched from a ground with an initial velocity of 352 ft./s how long will it take a rocket to reach its maxim
eduard
5.47 Seconds if my calculations are correct
4 0
3 years ago
What is the vertex of the parabola?<br><br> y+4=1/2(x−7)^2
babymother [125]
Y=a(x-h)²+k

y+4=1/2(x-7)²

y=1/2(x-7)²-4

(h,k) is the vertex

(7, -4)
7 0
4 years ago
Other questions:
  • 20 is what percent of 80?
    10·2 answers
  • Find the slope of the line. Write it as a fraction or an integer, not a decimal or a mixed number.
    7·1 answer
  • Are these correct? Cannot afford to fail this
    10·2 answers
  • Anyone know how to do this?
    5·1 answer
  • What is the product written in scientific notation? (1.18×10^3)⋅(9.1×10^−6)
    6·1 answer
  • Can someone help me on this really easy 6th grade math?
    12·1 answer
  • If 17 people voted for Jason as Vice President and 8 people voted for Karen as Vice President, what is the percent of votes for
    14·2 answers
  • Can someone please help me with this question, If you can thank you so much.
    14·2 answers
  • Pls help on any of these problems thankssss
    12·1 answer
  • What is the balance as a result of having a credit of $ 84 and a debit of $29
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!